Using your convention of naming, we do not know who Nicholas's father was, so if they followed convention we can assume he was a John. Ann Phillips father was a William, so we can assume that William was the second son. If they did have a 3rd son and followed convention, then there might have been a Nicholas Jr.
John is well documented from 1707 through 1759 when he disappeared from the records down in NC. William does not really start showing up in records until 1740 in a land deal. Nicholas Jr does not show up in any record at all. There is a land deal in 1741 that mentions that a Nicholas Christopher bought land for his sons John, William and Nicholas Jr. I think that is the New York Nicholas b.1703 who married Ann C Bowman in Richmond New York. And at that time John and William were grown men with their own families and land.
The remaining sons of Nicholas and Ann are David, Jacobus, and Robert all born after 1720 are well documented. There is a court record where a school master sued Nicholas in the 1730's for tuition for teaching 3 boys and I assume those are David, Jacobus, and Robert as they would all be under 10 years old.
As far as Nicholas Jr goes he is not mentioned in Nicholas Sr will. Elizabeth Ann McConnico died in 1735, I believe as I just studied the McConnico's yesterday because I never say any records of Nicholas and Ann having a daughter Elizabeth Ann. But William McConnico, his son Jared McConnico and Jared's Wife Keziah Witnessed the will of Nicholas in 1754. There had to be some connection. Also as I researched William McConnico I noticed that he was always in the same counties as Nicholas from the mid 1720's through his death in 1758 in Lunenburg County.